Topological lax comma categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914186922033152 |
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| author | Clementino, Maria Manuel Hofmann, Dirk Prezado, Rui |
| author_facet | Clementino, Maria Manuel Hofmann, Dirk Prezado, Rui |
| contents | This paper investigates the interplay between properties of a topological space $X$, in particular of its natural order, and properties of the lax comma category $\mathsf{Top} \Downarrow X$, where $\mathsf{Top}$ denotes the category of topologicalspaces and continuous maps. Namely, it is shown that, whenever $X$ is a topological $\bigwedge$-semilattice, the canonical forgetful functor $\mathsf{Top} \Downarrow X \to \mathsf{Top}$ is topological, preserves and reflects exponentials, and preserves effective descent morphisms. Moreover, under additional conditions on $X$, a characterisation of effective descent morphisms is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological lax comma categories Clementino, Maria Manuel Hofmann, Dirk Prezado, Rui Category Theory General Topology 06B30, 06B35, 06F30, 18A25, 18F60, 18F20, 22A26, 54B30 This paper investigates the interplay between properties of a topological space $X$, in particular of its natural order, and properties of the lax comma category $\mathsf{Top} \Downarrow X$, where $\mathsf{Top}$ denotes the category of topologicalspaces and continuous maps. Namely, it is shown that, whenever $X$ is a topological $\bigwedge$-semilattice, the canonical forgetful functor $\mathsf{Top} \Downarrow X \to \mathsf{Top}$ is topological, preserves and reflects exponentials, and preserves effective descent morphisms. Moreover, under additional conditions on $X$, a characterisation of effective descent morphisms is obtained. |
| title | Topological lax comma categories |
| topic | Category Theory General Topology 06B30, 06B35, 06F30, 18A25, 18F60, 18F20, 22A26, 54B30 |
| url | https://arxiv.org/abs/2504.12965 |